Question

Q.8. A wave y = a sin ($\omega$t - kx) on a string meets with another wave producing a node at x = 0. Then
the equation of the unknown wave is-
(1) y = a sin ($\omega$t + kx)
(2) y = - a sin ($\omega$t + kx)
(3) y = a sin ($\omega$t - kx)
(4) y = - a sin ($\omega$t - kx)

Answer 1

Dear Student ,

• Nodes and antinodes are formed in standing waves.
• Node is the point where the amplitude is zero or minimum and antinode is the point where the amplitude is maximum.
• For the formation of standing wave, the second wave should travel in opposite direction to the first wave, that is, in negative x direction. As the combination of the waves should result zero amplitude, the sign of the second wave must be negative.
• So, the equation of the unknown wave is $\mathrm{y}=-\mathrm{a}\sin \left(\mathrm{\omega t}+\mathrm{kx}\right)$

Regards